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R theAC Circuits: Oscillospes

Vanessa Breguez

Thomas Kincheloe

Group 1

PHY 114 7:30am Mondays

Section 81464

TA: Hank Lamm

11/8/2011

Abstract

The goal of these experiments was to determine the relationship between the RMA value and theamplitude of the voltage, the relationship of the period and the frequency of the signal and todetermine the resonance frequency of a driven RLC circuit throughthe exploration of the powerdissipated on the load resistor.

In Part I, the period was determined to be

, and the calculated frequency was 1000Hz.The DC offset from the oscilloscope was

, and through the DMM was

; the percentdifference was 5.87. The two values agreed. The

as measured from the oscilloscope was0.85V, and from the DMM it was 0.573V. The percent difference was determined to be 4.8%.The unknown frequency was found to be 2000Hz. The actual value was 1987Hz, with a 1%discrepancy.

The theoretical angular frequency

was calculated to

. The angular frequencyfrom the oscilloscope was

, form the graphical method it was 10

.The percent discrepancies were 1% and 0%, respectively. Both values were found to agree.

Thebiggest sources of error in these experiments came from the resistor, capacitor and the inductorwhich all had a 10% tolerance.

Objectives

The goal of this lab was to investigate the sine wave AZ signal from signal generator,thus determining the relationship between both the RMA value and the amplitude of the voltage,as well as the period of frequency of the signal. The resonant frequency was also determined fora driven RLD circuit from the exploration of the dissipated power on the load resistor. Some ofthe measurements taken included frequency (Hz) and voltage (V).

The circuit was connected as shown in Figure 1. The signal generator was set to a 1000Hz sinewave of magnitude about 1V measured on the DMM (AC). DMM on AC position read the RMSvalue. The cal knob on the signal generator was set to the calibrated position.The SEC/DIV wasadjusted on the scope to display one complete period of the measured waveform. The CAL knobwas clicked into the calibrated position. The periodT

of the wave was measured. The frequencywas given byf(Hz) = 1/T(sec). The frequency wascomputed and compared with the signalgenerator setting.

The scope was set to DC offset of zero, while the DMM (DC) was observed. The DMM waschanged to AC, and then the amplitude of the sine wave was determined from the scope traceand this was compared to the reading from the DMM.

The signal generator was then positioned in such a way that the frequency from the generatorwas not displayed (the displayed was covered). The frequency was changed by randomly rotatingthe frequency adjustment knob and the

unknown frequency was determined.

Part II

The circuit was connected as shown in Figure 2 using a load resistance

, acapacitor

, and inductance

. The AC power supply was turned on (signalgenerator) and it was set to a

sine wave mode about 1

and frequency 1000Hz. The RMSvalue was adjusted of a voltage value of 1

on the signal generator using the reading fromthe scope. Both waves were obtained on the scope simultaneously.

The resonant frequency

was found and recorded where the current through

was at amaximum (by measuring the voltage across it). Three independent readings were taken.

The voltage drop on the resistor versus frequencyf

were measured as the resonance was tunedthoughrange 800-3000 Hz. For each frequencyf

the average power dissipated was calculated inthe resistanceR. Resistance versus power was plotted in Graphical Analysis (GA). The data wasfit with the expression:

WhereA representsRMS voltage

, B represents resistanceR,

represents thecapacitanceC

of such value, angular frequency

is variable in the equation, represented byx.

Experimental Data

Part I

Period of oscilloscope:

.

Frequency: 10000Hz

DMM voltage: 0.0943 V

Oscilloscope voltage:

Amplitude of sine wave:

From scope: 0.85 V

From DMM: 0.573 V

Unknown frequency:

Using scope: 2000Hz

Generator display: 1987 Hz

Part II

Resonant frequency

: 1704Hz, 1699Hz, 1704Hz.

See attached Graph 1 and Graph 2.

Results

Part I

Source

Voltage (V)

% Difference

DMM

0.943

5.87

Oscilloscope

1.00

Table 1.Shows theDC offsetas gathered from the DMM and the oscilloscope, and comparesthe two values.

Source

Voltage (V)

% Difference

DMM

0.60

4.8

Oscilloscope

0.573

Table 2.Shows the

as gathered from the DMM and the oscilloscope, and compares the twovalues.

Unknown

Frequency (Hz)

% Discrepancy

Gathered from scope

1987

1

Generator display

2000

Table 3.Shows the unknown frequency as determined by the scope, and the actual value asgenerated in the display, as well as the percent discrepancy.

Part II

Source

Angular frequency

(Hz)

% Discrepancy (totheoretical)

% Error

Agrees?

Calculatedtheoretical

-

10

-

Oscilloscope(averaged)

1

0

Yes

Graph 2

0

0

Yes

Table4.Shows the values for the angular frequencies as gathered by the three different sources,and comparesthe values to the calculated theoretical,showing the errors, discrepancies, andwhether the values agree or not.

Discussion and Analysis

Part I

In Part I, the frequency was calculated from the period observed through the oscilloscope. Theperiod was determined to be

, and thecalculated frequency was 1000Hz. The displayalso read 1000Hz. This helped conclude that the oscilloscope reading was fairly accurate and thatcorrectly relates to the displayed frequency (frequency = 1/period).

Through Part I, theDC

offset was measured

through the oscilloscope as well as through theDMM reader. TheDC offsetvoltage as gathered through the oscilloscope was

, andthrough the DMM was

. The calculated percent difference was 5.87.

The two values werefound to be very closeto each other, as they should, since the DMM and oscilloscope weremeasuring the same thing.

TheRMS voltage

was measured through both the oscilloscope and DMM as well. The

as measured from the oscilloscope was measured to be 0.85V, and from the DMM it wasdetermined to be 0.573V. The percent difference between the two values was determined to be4.8%.This error is probably due to the misreading of the oscilloscope,or perhaps simply due tothe fact that the resistor and capacitor had a 10% tolerance.

The frequency generator display was covered for the last portion of Part I. A random frequencywas selected, and through reading the oscilloscope it was determined to be 2000Hz. Once thegenerator display was uncovered, the actual value of the “unknown” frequency was revealed tobe 1987Hz. The percent discrepancy between the observed value and the actual value wasdetermined to be 1.These values did agree very well, as they also should since they weremeasuring the same thing.

For all of these experiments, the biggest sources of errorcame from the resistor, capacitor andthe inductor. All three of these had a 10% tolerance to their values. A way a lot of this errorcould have been eliminatedwould be by actually measuring the resistance, capacitance, andinductance, reducing the error significantly, perhaps to even as low as 1%.

When analyzing the goals of the experiment, it can be seen that the relationship between theRMS value and the amplitude of the voltage was determined in Part I. The range on theoscilloscope (the

was measured and determined to be 1.7V. The equation

was usedto determine the height of the wave peak above zero voltage. Then it was determined that

√

, thus determining the relationship between

and amplitude.

The relationshipbetween frequency and period was

also studied in Part I. It was determined thatfrequencyf

is the inverse of timeT, or

.

Part II

The theoretical value of angular frequency

was calculated to be

whichtranslated to

. This high percent error is due to, once again, that the capacitorand the inductor values weren’t completely precise (having an error of 10%). The angularfrequency as gathered by directly measuring the resonant frequency off the oscilloscope was

. The

gathered using the graphical method was determined to be

. The percent discrepancies to the theoretical were determined to be 1% and 0%,respectively. Both values were found to agree with the theoretical since there was such a largerwindow of acceptance for values due to the 10% error on the theoretical value.

Part II helped determine the resonance frequency of a driven RLC circuit through the explorationof the power dissipated on the load resistor. Graph 3 shows this relationship as the data perfectlyfit Equation (1) that shows the relationship between resonance angular frequency and power.

The goal of these experimentswasto determine the relationship between the RMA value and theamplitude of the voltage, as well as the relationship of the period and the frequency of the signal.The resonance frequency of a driven RLC circuit was also determined through the exploration ofthe power dissipated on the load resistor.

In Part I, the period was determined to be

, and the calculated frequency

was 1000Hz.The display also read 1000Hz. The DC offset voltage as gathered through the oscilloscope was

, and through the DMM was

. The calculated percent difference was 5.87. The twovalues were found to agree. The

as measured from

the oscilloscope was measured to be0.85V, and from the DMM it was determined to be 0.573V. The percent difference between thetwo values was determined to be 4.8%.The unknown frequency was determined to be 2000Hz.The actual value was 1987Hz. The percent discrepancy between the observed value and theactual value was determined to be 1.

The theoretical value of angular frequency

was calculated to

. The angularfrequency as gathered from the oscilloscope was

, using the graphical method itwas determined to be

. The percent discrepancies to the theoretical weredetermined to be 1% and 0%, respectively. Both values were found to agree with the theoretical.

For all of these experiments, the biggest sources of error came from the resistor, capacitor andthe inductor. All three of these had a 10% tolerance to their values.